Question

AB and EDC are parallel lines.

BD = BC
Angle BDC = 55°
(a) (i) Work out the size of angle x.

...........................................................°
(ii) Give a reason for your answer.
.............................................................................................................................................
.............................................................................................................................................
(2)
(b) Find the size of angle y.



...........................................................°
(1)
(c) Work out the size of angle z.








...........................................................°

Answer 1

x = 125°, y = 55°, z = 70°

Explanation:

x and 55 are adjacent angles and are supplementary, sum to 180°, that is

x + 55° = 180° ( subtract 55° from both sides )

x = 125°

∠ ABD and ∠ BDC are alternate angles and congruent , so

y = 55°

Since BD and BC are congruent, then Δ BCD is isosceles, so

∠ BDC = ∠ BCD = 55° and

z = 180° - (55 + 55)° ← angle sum of triangle

= 180° - 110°

= 70°